Three‐dimensional controlled‐source electromagnetic modelling with a well casing as a grounded source: a hybrid method of moments and finite element scheme

Steel well casings in or near a hydrocarbon reservoir can be used as source electrodes in time‐lapse monitoring using grounded line electromagnetic methods. A requisite component of carrying out such monitoring is the capability to numerically model the electromagnetic response of a set of source electrodes of finite length. We present a modelling algorithm using the finite‐element method for calculating the electromagnetic response of a three‐dimensional conductivity model excited using a vertical steel‐cased borehole as a source. The method is based on a combination of the method of moments and the Coulomb‐gauged primary–secondary potential formulation. Using the method of moments, we obtain the primary field in a half‐space due to an energized vertical steel casing by dividing the casing into a set of segments, each assumed to carry a piecewise constant alternating current density. The primary field is then substituted into the primary–secondary potential finite‐element formulation of the three‐dimensional problem to obtain the secondary field. To validate the algorithm, we compare our numerical results with: (i) the analytical solution for an infinite length casing in a whole space, excited by a line source, and (ii) a three‐layered Earth model without a casing. The agreement between the numerical and analytical solutions demonstrates the effectiveness of our algorithm. As an illustration, we also present the time‐lapse electromagnetic response of a synthetic model representing a gas reservoir undergoing water flooding.     

Fast and accurate three‐dimensional controlled source electromagnetic modelling†

We present a fast approximate method for three‐dimensional low frequency controlled source electro‐magnetic modeling. We apply the method to a synthetic model in a typical marine controlled source electromagnetic scenario, where conductivity and permittivity are different from the known background medium. For 3D configurations, fast computational methods are relevant for both forward and inverse modelling studies. Since this problem involves a large number of unknowns, it has to be solved efficiently to obtain results in a timely manner, without compromising accuracy. For this reason, the Born approximation, extended Born approximation and iterative extended Born approximation are implemented and compared with the full solution of the conjugate gradient fast Fourier transformation method. These methods are based on an electric field domain integral equation formulation. It is shown here how well the iterative extended Born approximation method performs in terms of both accuracy and speed with different configurations and different source positions. The improved accuracy comes at virtually no additional computational cost. With the help of this method, it is now possible to perform sensitivity analysis using 3D modelling in a timely manner, which is vital for controlled source electromagnetic applications. For forward modeling the solution at the sea‐bottom is of interest, because that is where the receivers are usually located. For inverse modeling, the accuracy of the solution in the target zone is important to obtain reasonably accurate conductivity values from the inversion using this approximate solution method. Our modelling studies show that the iterative extended Born approximation method is fast and accurate for both forward and inverse modelling. Sensitivity analysis as a function of the source position and different reservoir sizes validate the accuracy of the iterative extended Born approximation.     

电导率各向异性的海洋电磁三维有限单元法正演

本文提出了一种基于非结构化网格的海洋电磁有限单元正演算法.为了回避场源奇异性, 文中选用二次场算法, 将背景电阻率设置为水平层状且各向异性, 场源在水平层状各向异性介质中所激发的一次场通过汉克尔积分得到.基于Coulomb规范得到二次矢量位和标量位所满足的Maxwell方程组, 通过Galerkin加权余量法形成大型稀疏有限元方程, 采用不完全LU分解(ILU)预条件因子的quasi-minimum residual(QMR)迭代解法对有限元方程进行求解得到二次矢量位和标量位; 进而, 利用滑动平均方法得到二次矢量位和标量位在空间的导数, 由此得到二次电磁场; 通过一维模型对算法的可靠性进行验证, 与此同时, 针对实际复杂海洋电磁模型, 比较有限元模拟结果与积分方程模拟结果, 进一步验证算法精度.若干计算结果均表明, 文中算法具有良好的通用性, 适用于井中电磁、航空电磁, 环境地球物理等非均匀且各向异性介质中的电磁感应基础研究.     

基于并行化直接解法的频率域可控源电磁三维正演

电磁法的三维数值模拟是一个对数值算法和计算机硬件要求都非常高的问题.对常用的微分类方法如有限单元法和有限差分法而言, 求解最后所得的大型线性方程组是至关重要的一步, 直接影响到正演算法的实用性.如何高效、稳定且准确地解线性方程长期以来一直是被探讨的问题.本文实现了基于线性系统直接求解技术的频率域可控源电磁(CSEM)三维正演.使用交错网格有限体积法(FV)来离散化关于二次电场的 Helmholtz 方程; 使用直接解法取代传统的迭代解法来求解离散线性系统, 即对系统矩阵进行完全LU分解, 具体通过调用大规模并行矩阵直接求解器(MUMPS)来实现.基于理论模型做了一系列数值实验, 首先证明了直接解法的高精度和稳定性, 并考察了其内存需求、计算时间和并行可伸缩性等主要计算性能, 最后检验了所开发的算法快速模拟多场源 CSEM 问题的能力以及对常规海洋和陆地CSEM模拟的有效性.     

Inversion of inline and broadside marine controlled‐source electromagnetic data with constraints derived from seismic data

We present a structural smoothing regularization scheme in the context of inversion of marine controlled‐source electromagnetic data. The regularizing hypothesis is that the electrical parameters have a structure similar to that of the elastic parameters observed from seismic data. The regularization is split into three steps. First, we ensure that our inversion grid conforms with the geometry derived from seismic. Second, we use a seismic stratigraphic attribute to define a spatially varying regularization strength. Third, we use an indexing strategy on the inversion grid to define smoothing along the seismic geometry. Enforcing such regularization in the inversion will encourage an inversion result that is more intuitive for the interpreter to deal with. However, the interpreter should also be aware of the bias introduced by using seismic data for regularization. We illustrate the method using one synthetic example and one field data example. The results show how the regularization works and that it clearly enforces the structure derived from seismic data. From the field data example we find that the inversion result improves when the structural smoothing regularization is employed. Including the broadside data improves the inversion results even more, due to a better balancing between the sensitivities for the horizontal and vertical resistivities.     

Three‐dimensional inversion of towed streamer electromagnetic data

A towed streamer electromagnetic system capable of simultaneous seismic and electromagnetic data acquisition has recently been developed and tested in the North Sea. We introduce a 3D inversion methodology for towed streamer electromagnetic data that includes a moving sensitivity domain. Our implementation is based on the 3D integral equation method for computing responses and Fréchet derivatives and uses the re‐weighted regularized conjugate gradient method for minimizing the objective functional with focusing regularization. We present two model studies relevant to hydrocarbon exploration in the North Sea. First, we demonstrate the ability of a towed electromagnetic system to detect and characterize the Harding field, a medium‐sized North Sea hydrocarbon target. We compare our 3D inversion of towed streamer electromagnetic data with 3D inversion of conventional marine controlled‐source electromagnetic data and observe few differences between the recovered models. Second, we demonstrate the ability of a towed streamer electromagnetic system to detect and characterize the Peon discovery, which is representative of an infrastructure‐led shallow gas play in the North Sea. We also present an actual case study for the 3D inversion of towed streamer electromagnetic data from the Troll field in the North Sea and demonstrate our ability to image all the Troll West Oil and Gas Provinces and the Troll East Gas Province. We conclude that 3D inversion of data from the current generation of towed streamer electromagnetic systems can adequately recover hydrocarbon‐bearing formations to depths of approximately 2 km. We note that by obviating the need for ocean‐bottom receivers, the towed streamer electromagnetic system enables electromagnetic data to be acquired over very large areas in frontier and mature basins for higher acquisition rates and relatively lower cost than conventional marine controlled‐source electromagnetic methods.     

考虑海底地形的三维频率域可控源电磁响应有限体积法模拟

为了提高海洋可控源电磁的地形响应模拟精度,探讨了三维交错网格剖分有限体积法求解频率域电磁场解的数值方法.在似稳场近似条件下,推导了有限差分法和有限体积法低频电磁场控制方程的离散表达式.通过对离散表达式的分析比较表明,有限体积法较之有限差分具有更高的计算精度,同时也具有与有限差分相当的计算效率.对含地形界面网格单元电导率采用加权平均处理,通过与二维有限元程序的计算结果对比,验证了该方法可以有效提高有限体积法对地形变化的模拟精度.应用有限体积法计算了一个三维带地形储层模型的可控源电磁响应,分析表明地形变化对电场分量影响明显,磁场分量对地形变化不敏感.     

A land controlled‐source electromagnetic experiment using a deep vertical electric dipole: experimental settings,processing, and first data interpretation

A multichannel borehole‐to‐surface controlled‐source electromagnetic experiment was carried out at the onshore CO₂ storage site of Hontomín (Spain). The electromagnetic source consisted of a vertical electric dipole located 1.5 km deep, and the electric field was measured at the surface. The subsurface response has been obtained by calculating the transfer function between the transmitted signal and the electric field at the receiver positions. The dataset has been processed using a fast processing methodology, appropriate to be applied on controlled‐source electromagnetics (CSEM) data with a large signal‐to‐noise ratio. The dataset has been analysed in terms of data quality and repeatability errors, showing data with low experimental errors and good repeatability. We evaluate if the induction of current along the casing of the injection well can reproduce the behaviour of the experimental data.     

2.5D direct‐current resistivity forward modelling and inversion by finite‐element–infinite‐element coupled method

To reduce the numerical errors arising from the improper enforcement of the artificial boundary conditions on the distant surface that encloses the underground part of the subsurface, we present a finite‐element–infinite‐element coupled method to significantly reduce the computation time and memory cost in the 2.5D direct‐current resistivity inversion. We first present the boundary value problem of the secondary potential. Then, a new type of infinite element is analysed and applied to replace the conventionally used mixed boundary condition on the distant boundary. In the internal domain, a standard finite‐element method is used to derive the final system of linear equations. With a novel shape function for infinite elements at the subsurface boundary, the final system matrix is sparse, symmetric, and independent of source electrodes. Through lower upper decomposition, the multi‐pole potentials can be swiftly obtained by simple back‐substitutions. We embed the newly developed forward solution to the inversion procedure. To compute the sensitivity matrix, we adopt the efficient adjoint equation approach to further reduce the computation cost. Finally, several synthetic examples are tested to show the efficiency of inversion.     

Inversion of controlled‐source electromagnetic data using a model‐based approach

A two‐and‐half dimensional model‐based inversion algorithm for the reconstruction of geometry and conductivity of unknown regions using marine controlled‐source electromagnetic (CSEM) data is presented. In the model‐based inversion, the inversion domain is described by the so‐called regional conductivity model and both geometry and material parameters associated with this model are reconstructed in the inversion process. This method has the advantage of using a priori information such as the background conductivity distribution, structural information extracted from seismic and/or gravity measurements, and/or inversion results a priori derived from a pixel‐based inversion method. By incorporating this a priori information, the number of unknown parameters to be retrieved becomes significantly reduced. The inversion method is the regularized Gauss‐Newton minimization scheme. The robustness of the inversion is enhanced by adopting nonlinear constraints and applying a quadratic line search algorithm to the optimization process. We also introduce the adjoint formulation to calculate the Jacobian matrix with respect to the geometrical parameters. The model‐based inversion method is validated by using several numerical examples including the inversion of the Troll field data. These results show that the model‐based inversion method can quantitatively reconstruct the shapes and conductivities of reservoirs.     

复杂场源形态的海洋可控源电磁三维正演

在使用电偶极发射源的可控源电磁法(CSEM)勘探中,发射源的方位、长度、形状等对观测数据有重要的影响,然而现有的大部分三维数值模拟方法没有全面地将这些因素考虑进来,很多都只能应对非常简单的场源形态,例如单一方位的点电偶极子,这有可能显著降低模拟结果的准确性.本文实现了基于交错网格有限体积(FV)离散的海洋CSEM三维正演算法,能够模拟形态相对复杂的场源,包括任意方位的有限长直导线和弯曲导线发射源.该算法使用一次场/二次场方法,只需对二次场使用FV法求解,避免了场源的奇异性问题;一次场的计算为一维正演问题,使用准解析法求解,并且只要在计算一次场时考虑复杂的场源形态便可以实现同样场源的三维正演.通过与一维理论模型的解析解对比验证了三维程序的准确性,并针对三维理论模型进行了一系列正演测试,初步考察了场源形态对三维正演结果的影响.     

Three‐dimensional modelling of magnetotelluric data to image Sehqanat hydrocarbon reservoir in southwestern Iran

A detailed magnetotelluric survey was conducted in 2013 in the Sehqanat oil field, southwestern Iran to map the geoelectrical structures of the sedimentary Zagros zone, particularly the boundary between the Gachsaran Formation acting as cap rock and the Asmari Formation as the reservoir. According to the electrical well logs, a large resistivity contrast exists between the two formations. The Gachsaran Formation is formed by tens to hundreds of metres of evaporites and it is highly conductive (ca. 1 Ωm–10 Ωm), and the Asmari Formation consists of dense carbonates, which are considerably more resistive (more than 100 Ωm). Broadband magnetotelluric data were collected along five southwest–northeast directed parallel lines with more than 600 stations crossing the main geological trend. Although dimensionality and strike analysis of the magnetotelluric transfer functions showed that overall they satisfied local 2D conditions, there were also strong 3D conditions found in some of the sites. Therefore, in order to obtain a more reliable image of the resistivity distribution in the Sehqanat oil field, in addition to standard 2D inversion, we investigated to what extent 3D inversion of the data was feasible and what improvements in the resistivity image could be obtained. The 2D inversion models using the determinant average of the impedance tensor depict the main resistivity structures well, whereas the estimated 3D model shows significantly more details although problems were encountered in fitting the data with the latter. Both approaches resolved the Gachsaran–Asmari transition from high conductivity to moderate conductivity. The well‐known Sehqanat anticline could also be delineated throughout the 2D and 3D resistivity models as a resistive dome‐shaped body in the middle parts of the magnetotelluric profiles.     

Three‐dimensional modeling of coastal boulders using multi‐view image measurements

Coarse clastic sediments (boulders) on coastlines have seen a groundswell in geomorphic research interest over recent years, associated in part with the potential of boulder evidence for interpreting characteristics of high‐energy wave processes. Yet, the fundamental property of boulder volume is normally difficult to measure accurately owing to complex clast morphology and irregular surface texture. To tackle this problem, this paper concentrates on creating precise, measurable and textured three‐dimensional (3D) models of coastal boulders without physical contact with the object, based on multi‐view image measurement techniques. This method has several advantages over traditional measurements that are inaccurate or alternative solutions using costly techniques such as terrestrial laser scanning. Our methods propose the use of low‐cost equipment (digital cameras) that can be used in various coastal environments to easily acquire numerous images of the object of interest. Initial results can be rapidly assessed in the field for immediate quality control. Resulting 3D models, built from overlapping multi‐view digital photographs, allow the reconstruction of realistic‐looking and textured boulder surfaces. A particular interest in this task is the family of algorithms known as structure from motion (SFM). The work presents analysis of SFM techniques by examining 3D models of boulders observed at a coastal field site on Lu Dao Island in south‐eastern Taiwan. Copyright © 2013 John Wiley & Sons, Ltd.     

Wavenumber of the guided wave supported by a thin resistive layer in marine controlled‐source electromagnetics

This paper discusses the asymptotic behaviour of the electromagnetic fields received on the sea‐bed (target response), as well as the fields distributed inside a thin resistive target, generated by a horizontal electric dipole above the sea‐bed in marine controlled‐source electromagnetics for hydrocarbon exploration. It is found that the guided wave supported by a thin resistive target can be expressed as a single‐mode exponential function. A simple closed‐form expression is derived to relate the single‐mode wavenumber of the guided wave to the model parameters: the resistivity and thickness of the target layer, the sea‐bed resistivity and the frequency. When the air‐wave is removed, the guided wave is dominant among the fields received on the sea‐bed at far offset. Hence the wavenumber of the guided wave can be calculated from the fields measured on the sea‐bed. The closed‐form expression can then be used to invert the target property from the calculated wavenumber and hence, can be considered as a hydrocarbon indicator.     

RC pile–soil interaction analysis using a 3D‐finite element method with fibre theory‐based beam elements

To evaluate the overall response of a structural system including its foundation and surrounding soil, an equivalent finite element model with reduced degrees of freedom using fibre theory‐based beam element was proposed. The proposed model was based on investigations of the subgrade soil reaction of a single‐layer model, and was verified for the cyclic behaviour of a laterally loaded single RC pile in terms of the load–displacement relationship, pile deformation, and soil pressures on the pile surface. Also investigated was the effect of the interfacial element between pile and soil on the behaviour of the laterally loaded pile. Copyright © 2006 John Wiley & Sons, Ltd.     

Controlled‐source electromagnetic monitoring of reservoir oil saturation using a novel borehole‐to‐surface configuration

To advance and optimize secondary and tertiary oil recovery techniques, it is essential to know the areal propagation and distribution of the injected fluids in the subsurface. We investigate the applicability of controlled‐source electromagnetic methods to monitor fluid movements in a German oilfield (Bockstedt, onshore Northwest Germany) as injected brines (highly saline formation water) have much lower electrical resistivity than the oil within the reservoir. The main focus of this study is on controlled‐source electromagnetic simulations to test the sensitivity of various source–receiver configurations. The background model for the simulations is based on two‐dimensional inversion of magnetotelluric data gathered across the oil field and calibrated with resistivity logs. Three‐dimensional modelling results suggest that controlled‐source electromagnetic methods are sensitive to resistivity changes at reservoir depths, but the effect is difficult to resolve with surface measurements only. Resolution increases significantly if sensors or transmitters can be placed in observation wells closer to the reservoir. In particular, observation of the vertical electric field component in shallow boreholes and/or use of source configurations consisting of combinations of vertical and horizontal dipoles are promising. Preliminary results from a borehole‐to‐surface controlled‐source electromagnetic field survey carried out in spring 2014 are in good agreement with the modelling studies.     

A new marine controlled‐source electromagnetic receiver with an acoustic telemetry modem and arm‐folding mechanism

We developed a new marine controlled‐source electromagnetic receiver for detecting methane hydrate zones and oil and gas reservoirs on the seafloor, which is not imaged well by seismic reflection surveys. To determine the seafloor structure, the electromagnetic receiver should have low noise, power consumption, clock drift error, and operating costs while being highly reliable. Because no suitable receiver was available in our laboratory, we developed a new marine controlled‐source electromagnetic receiver with these characteristics; the receiver is equipped with acoustic telemetry modem and an arm‐folding mechanism to facilitate deployment and recovering operations. To demonstrate the applicability of our new receiver, we carried out a field experiment offshore of Guangzhou in the South China Sea, where methane hydrates have been discovered. We successfully obtained controlled‐source electromagnetic data along a profile about 13 km long. All six new receivers were recovered, and high‐quality electromagnetic data were obtained. Relatively high apparent resistivity values were detected. The results of the offshore field experiment support the claim that the electromagnetic data obtained using the new receiver are of sufficient quality for the survey target.     

Two‐dimensional hydraulic flood modelling using a finite‐element mesh decomposed according to vegetation and topographic features derived from airborne scanning laser altimetry

Airborne scanning laser altimetry (LiDAR) is an important new data source that can provide two‐dimensional river flood models with spatially distributed floodplain topography for model bathymetry, together with vegetation heights for parameterization of model friction. Methods are described for improving such models by decomposing the model's finite‐element mesh to reflect floodplain vegetation features such as hedges and trees having different frictional properties to their surroundings, and significant floodplain topographic features having high height curvatures. The decomposition is achieved using an image segmentation system that converts the LiDAR height image into separate images of surface topography and vegetation height at each point. The vegetation height map is used to estimate a friction factor at each mesh node. The spatially distributed friction model has the advantage that it is physically based, and removes the need for a model calibration exercise in which free parameters specifying friction in the channel and floodplain are adjusted to achieve best fit between modelled and observed flood extents. The scheme was tested in a modelling study of a flood that occurred on the River Severn, UK, in 1998. A satellite synthetic aperture radar image of flood extent was used to validate the model predictions. The simulated hydraulics using the decomposed mesh gave a better representation of the observed flood extent than the more simplistic but computationally efficient approach of sampling topography and vegetation friction factors on to larger floodplain elements in an undecomposed mesh, as well as the traditional approach using no LiDAR‐derived data but simply using a constant floodplain friction factor. Use of the decomposed mesh also allowed velocity variations to be predicted in the neighbourhood of vegetation features such as hedges. These variations could be of use in predicting localized erosion and deposition patterns that might result in the event of a flood. Copyright © 2003 John Wiley & Sons, Ltd.